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Simplifying 90 = -16t2 + 50t + 90 Reorder the terms: 90 = 90 + 50t + -16t2 Add '-90' to each side of the equation. 90 + -90 = 90 + 50t + -90 + -16t2 Combine like terms: 90 + -90 = 0 0 = 90 + 50t + -90 + -16t2 Reorder the terms: 0 = 90 + -90 + 50t + -16t2 Combine like terms: 90 + -90 = 0 0 = 0 + 50t + -16t2 0 = 50t + -16t2 Solving 0 = 50t + -16t2 Solving for variable 't'. Remove the zero: -50t + 16t2 = 50t + -16t2 + -50t + 16t2 Reorder the terms: -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -50t + 16t2 = 0 + -16t2 + 16t2 -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-25 + 8t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-25 + 8t)' equal to zero and attempt to solve: Simplifying -25 + 8t = 0 Solving -25 + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 8t = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 8t = 0 + 25 8t = 0 + 25 Combine like terms: 0 + 25 = 25 8t = 25 Divide each side by '8'. t = 3.125 Simplifying t = 3.125Solution
t = {0, 3.125}
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